Inverse boundary value problems for polyharmonic operators with non-smooth coefficients

TL;DR

This paper advances inverse boundary value problem solutions for polyharmonic operators by relaxing regularity conditions on coefficients, employing an averaging technique to establish uniqueness.

Contribution

It introduces a novel approach that reduces regularity requirements for coefficient recovery in polyharmonic inverse problems.

Findings

Uniqueness of coefficient recovery under lower regularity assumptions

Extension of techniques from second order to polyharmonic operators

Application of Haberman and Tataru's averaging method

Abstract

We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.